Specialization at T = 400/29 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -8921224827903176421867T^8 + 94634723251967943349008T^7 - 153371039643193058472636T^6 - 641050270990816586343840T^5 - 1411956329363864664615090T^4 - 3616744002660872511746400T^3 - 276286449215617413614716T^2 + 3264390669786107213517648T - 1094619040863704280589707,
A6 = 270621608798713355418362188083174T^12 - 4440334258578316878189533038482864T^11 + 26574225298655897363019125632965972T^10 - 44466546059753405576217220076774400T^9 - 266551804859294565919720379747154006T^8 + 857066304185931807663129817734860208T^7 + 2882807104710383577362230811059875192T^6 + 490875434163168933481957024140491568T^5 - 2474513386731796364719321202224339446T^4 + 1633690238596691275986648934120443840T^3 + 1554365531979876509922013707743895892T^2 - 1882445996339364406394564636163936624T + 453429930884494956186985826996791494.
It is a 2-neighbour of the fibration given in curve#3900: its Mordell-Weil lattice (rank 17, no reducible fibres) is a root-free Kneser 2-neighbour of that fibration's, realised by the pencil |O + P - F| for a section P of height 12. Constructed and searched by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.
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